Place chicken breasts in a zip-top bag and pound to an even thickness with a meat mallet or rolling pin. Remove from the bag and pat completely dry with paper towels. Season both sides with salt, pepper, and Italian seasoning.

Heat olive oil in a large skillet over medium-high heat. Add the chicken and cook 5 to 7 minutes per side until golden brown and the internal temperature reads 165°F on an instant-read thermometer. Cover the pan if needed for thicker breasts. Transfer to a clean plate and tent loosely with foil.

Reduce heat to medium. Add butter and shallots to the same skillet. Cook 1 to 2 minutes, stirring, until shallots are soft and translucent.

Add the garlic and flour. Stir constantly for 1 minute to cook out the raw flour taste.

Pour in the chicken broth and scrape up any browned bits from the bottom of the pan. Stir often and cook 2 to 3 minutes until the sauce thickens slightly.

Reduce heat to medium-low. Stir in the sun-dried tomatoes and fresh spinach. Cook 1 to 2 minutes until the spinach wilts. Pour in the heavy cream and stir to combine.

Return the chicken to the skillet. Spoon the sauce over each breast and heat 1 to 2 minutes until warmed through. Serve immediately with grated Parmesan cheese on top if desired.